A scarf is of the shape of an isosceles right angled triangle. each of

1.	A scarf is of the shape of an isosceles right angled triangle. each of the equal side is 90 cm . how much cloth will be needed to prepare 8 such scarf? also find the cost of the cloth at the rate of Rs.40 per cm^2.
Answer» Given : A scarf is of the shape of an isosceles right angled TRIANGLE with equal sides 90cm ( refer the attachment for figure ). To find : The cloth that will be needed for preparing 8 such scarf. The cost of the cloth at the rate of RS. 40 PER cm² Solution : $\sf Cloth \: that \: will \: be \: needed \: for \: 8 \: such \: scarf : \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \bf 8 \times area \: of \: the \: scarf$ $\sf Area \: of \: the \: scarf = \dfrac{1}{2} \times b \times h$ Here, BASE and HEIGHT are the same (90cm) $\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf = \frac{1}{ \cancel{ \: 2 \: }} \times \cancel{90} \: \: ^{45} \times 90 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf = 45 \times 90 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf = \blue{ \underline{ \boxed{ \sf{ \pmb {4050 \: {cm}^{2} }}}}}$ $\sf \therefore \sf Cloth \: that \: will \: be \: needed \: for \: 8 \: such \: scarf : \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \bf 8 \times area \: of \: the \: scarf \\ \sf \implies 8 \times 4050 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf \implies \blue{ \underline{ \boxed{ \sf{ \pmb {32400 \: {cm}^{2} }}}}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$ $\sf Cost \: of \: the \: cloth \: at \: \: \bf{Rs. \: 40 \: per \: cm^{2} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf = 40 \times area \: of \: the \: total \: cloth \\ \sf = 40 \times 32400 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf = \blue{ \underline{ \boxed{ \sf{ \pmb {Rs. \: 1296000 }}}}} \: \: \: ~~~~~~~~~~~~~~ \: \: \: \: \: \:$ ∴ Required answer : Area of 8 such scarfs = 32,400cm² Cost of the total cloth at Rs. 40 per cm² = Rs. 12,96,000

A scarf is of the shape of an isosceles right angled triangle. each of the equal side is 90 cm . how much cloth will be needed to prepare 8 such scarf? also find the cost of the cloth at the rate of Rs.40 per cm^2.

Answer»

Given :

A scarf is of the shape of an isosceles right angled TRIANGLE with equal sides 90cm ( refer the attachment for figure ).

To find :

The cloth that will be needed for preparing 8 such scarf.
The cost of the cloth at the rate of RS. 40 PER cm²

Solution :

$\sf Cloth \: that \: will \: be \: needed \: for \: 8 \: such \: scarf : \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \bf 8 \times area \: of \: the \: scarf$

$\sf Area \: of \: the \: scarf = \dfrac{1}{2} \times b \times h$

Here, BASE and HEIGHT are the same (90cm)

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf = \frac{1}{ \cancel{ \: 2 \: }} \times \cancel{90} \: \: ^{45} \times 90 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf = 45 \times 90 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf = \blue{ \underline{ \boxed{ \sf{ \pmb {4050 \: {cm}^{2} }}}}}$

$\sf \therefore \sf Cloth \: that \: will \: be \: needed \: for \: 8 \: such \: scarf : \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \bf 8 \times area \: of \: the \: scarf \\ \sf \implies 8 \times 4050 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf \implies \blue{ \underline{ \boxed{ \sf{ \pmb {32400 \: {cm}^{2} }}}}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\sf Cost \: of \: the \: cloth \: at \: \: \bf{Rs. \: 40 \: per \: cm^{2} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf = 40 \times area \: of \: the \: total \: cloth \\ \sf = 40 \times 32400 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf = \blue{ \underline{ \boxed{ \sf{ \pmb {Rs. \: 1296000 }}}}} \: \: \: ~~~~~~~~~~~~~~ \: \: \: \: \: \:$