In figure BD = 10 cm Ac = 12 cm and bc = 26 cm A) find area of abc b)

1.	In figure BD = 10 cm Ac = 12 cm and bc = 26 cm A) find area of abc b) Calculate the height AEin figure BD = 10 cm Ac = 12 cm and bc = 26 cm A) find area of abc b) Calculate the height AE ( Figure given below)
Answer» Given: In FIGURE BD = 10 cm AC = 12 cm and BC = 26 cm To find: A) Area of ABC B) The height AE Solution: Finding the value of AD: In Δ BDC, using Pythagoras theorem, we get $BC^2 = CD^2 + BD^2$ $\implies 26^2 = (12 + AD)^2 + 10^2$ $\implies 676 = (12 + AD)^2 + 100$ $\implies 576 = (12 + AD)^2$ $\implies 24 = 12 + AD$ $\implies \bold{AD = 12 \:cm}$ Finding the value of AB: In Δ ABD, using Pythagoras theorem, we get $AB^2 = AD^2 + BD^2$ $\implies AB = \sqrt{AD^2 + AD^2}$ $\implies AB = \sqrt{12^2 + 10^2}$ $\implies \bold{ AB = 15.62\:cm}$ Finding the area of Δ ABC: Using Heron's formula in Δ ABC, we have a = 15.62 cm, b = 12 cm & c = 26 cm Semi-perimeter, S = $\frac{a+b+c}{2} = \frac{15.62 + 12 + 26}{2} = \frac{53.62}{2} = 26.81 \:cm$ ∴ Area of Δ ABC, = $\sqrt{s (s - a) (s -b)(s-c)}$ = $\sqrt{26.81 (26.81 - 15.62) (26.81 - 12)(26.81-26)}$ = $\sqrt{26.81 \times 11.19 \times 14.81 \times 0.81}$ = $59.99$ ≈ $\boxed{\bold {60 \: cm}}$ Finding the height AE: We know, $\boxed{\bold{Area \:of\:a\:triangle = \frac{1}{2} \times base \times height}}$ ∴ Area of Δ ABC = $\frac{1}{2} \times BC \times AE$ $\implies 60 = \frac{1}{2} \times 26 \times AE$ $\implies 60 = 13 \times AE$ $\implies AE = \frac{60}{13}$ $\implies \boxed{\bold{AE =4.6\: cm}}$ -------------------------------------------------------------------------------------- Also View: In the ADJOINING figure, find the area of triangle ABC brainly.in/question/11964151 Find the area of triangle ABC, right-angled at B and AB and BC measuring 16cm and 10 cm respectively. brainly.in/question/6755539 Determine the area of triangle ABC with AC=5cm and height DB=30mm brainly.in/question/12182933 Find BC if the area of the triangle ABC is 36 CM square and the height it is 3 cm brainly.in/question/7425494