Question

The perimeter of an isosceles right triangle is 24 cm. If its hypotenuse is 10 cm, find the other two sides. Find its area by using the formula area of a right triangle. Verify your result by using Heron’s formula.25 POINTS ON THE LINE FOR WHO CAN ANSWER,BE QUICK.

Answer 1

Answer:

answer =24 square centimetres

Step-by-step explanation:

Let ABC is a right angled triangle.

i) Perimeter of ∆ABC = 24

=> x+y+10=24

=> x+y = 24-10

=> x+y = 14 ---(1)

ii)By Phythagorean theorem:

AC²= AB²+BC²

=> 10²= x² + y²

=> x²+y² = 100 ---(2)

iii) On Squaring equation (1), we get

=> (x+y)² = 14²

=> x²+y²+2xy = 196

=> 100+2xy = 196

/* From (2) */

=> 2xy = 196-100

=> 2xy = 96

/* Divide both sides by 2 , we get

=> xy = 48 ---(3)

Now ,

Area of triangle ABC=1/2×AB×BC

=1/2(xy)

=1/2×48

=24 square centimetres

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Answer 2

kindly check the attachment for the stepwise solution and answer.