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The sides of a right-angled triangle containing the right angle are 4x and (2x - 1) cm. If the area of the triangle is 30cm². Calculate the length of its sides. |
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Answer» N: Here we have been provided with sides of a right-angled triangle. First side = 4x Second side = 2x - 1 And area is of 30cm².We have to CALCULATE the lengths of its sides. So we would be USING formula of calculating the area of triangle,A = 1/2 × b × H Here, h is height and b is base.We have, base = 2x-1 and height = 4xSo using this formula, ⇒30 = 1/2 × (2x - 1) × 4x ⇒ 30 = 1 × (2x - 1) × 2x ⇒ 30 = 2x (2x - 1) Opening bracket, ⇒ 30 = 2x × (2x - 1) ⇒ 30 = 4x² - 2x DIVIDING by 2, ⇒ 15 = 2x² - x Transposing 15 to R.H.S., ⇒ 2x² - x - 15 = 0 Forming factors, ⇒ 2x² - 6x + 5x - 15 = 0 Grouping them, ⇒ 2x (x - 3) + 5 (x - 3) = 0 ⇒ (x - 3) (2x + 5) = 0 Now, ⇒ x - 3 = 0 ⇒ x = 3AND, ⇒ 2x + 5 = 0 ⇒ 2x = -5 ⇒ x = -5/2 We know that length is never negative.First side : 4x ⇒ 4 × 3 ⇒ 12cm Second side : 2x - 1 ⇒ 2 × 3 - 1 ⇒6 - 1 ⇒ 5cm We would be using Pythagoras theorem now, to find the third side, Third side : √12² + 5² ⇒√144 + 25⇒√169⇒13cm |
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