Question

if each equal said of an isosceles triangle XYZ is10cm and length of base is 4cm. let us write by calculating the area of ∆XYZ.​

Answer 1

XY (a) = 10 cm

YZ (b) = 10cm

ZX (c) = 4cm

Semi perimeter (s)= $\frac{a+b+c}{2}$

                          = $\frac{10+10+4}{2} = \frac{24}{2} = 12cm$

Area = √s×(s-a)×(s-b)×(s-c)

⇒ √12× (12-10)× (12-10)× (12-4)

⇒√12×2×2×8

Factorize the numbers, 12 = 2×2×3 , 2 = 2 , 2 = 2 , 8 = 2×2×2

⇒√2×2×3×2×2×2×2×2

Group 2 same numbers and then take 1 number from each pair out of the square root. The numbers that are without the pair, let them be in the square root. For example : √a×a×a = a√a, made the pair of 2as and the 3rd a, as it does not have a pair should be in the root.

⇒2×2×2√2×3

⇒8√6cm²

Final Answer:

Area = 8√6cm²