Question

2. The square of the hypotenuse of an isosceles right angled triangle is 242 cm². What is the length of
each equal side?​

Answer 1

Square of Hypotenuse =242cm^2

Let the equal sides be x cm.

According to pythagoras Theorem,

${hypotenuse}^{2} = {base}^{2} + {height}^{2} \\ 242 = {x}^{2} + {x}^{2} \\ 242 = 2 {x}^{2} \\ 141 = {x}^{2} \\ x = \sqrt{141}$

Therefore the length of the two equal sides are √141cm .

Hope it is helpful

Answer 2

Given:

Square of Hypotenuse of an isosceles triangle = 242$cm^2$

To Find:

Length of Perpendicular and Base of the same isosceles triangle.

Answer:

Let the perpendicular of the triangle be a.

Since,

In an isosceles triangle, the perpendicular and the base are equal .

Therefore,

Base = Perpendicular = a

From Pythagoras Theorem,

$\tt(hypotenuse)^{2} = (base)^{2} + (perpendicular)^{2} \\ \\\tt h^{2}={b}^{2} + p^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

In the question,

$h^2$ = 242 $cm^2$

Substituting the value , we get:

$\sf242 \: {cm}^{2} = {a}^{2} + {a}^{2} \\ \\ \sf242 \: {cm}^{2} = 2 {a}^{2} \: \: \: \: \: \: \: \: \\ \\\sf {a}^{2} = \dfrac{242}{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\\ \\ \sf {a}^{2} = 121 \: {cm}^{2} \: \: \: \: \: \: \: \: \: \: \\ \\\sf a = \sqrt{121 \: {cm}^{2} } \: \: \: \: \: \: \: \: \: \\ \\ \sf a = 11 \: cm \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Since base and perpendicular are equal.

Therefore, the answer is:

Base = 11 cm

Perpendicular = 11 cm