In an isosceles right-angled triangle, the le | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let the two equal sides of the isosceles right-angled triangle be $x$.According to the Pythagorean theorem, $x^2 + x^2 = (	ext{hypotenuse})^2$.Gi

Vedclass · Accepted Answer

$144$

Vedclass · Answer

(C) Let the two equal sides of the isosceles right-angled triangle be $x$.According to the Pythagorean theorem, $x^2 + x^2 = (	ext{hypotenuse})^2$.Given the hypotenuse is $24$, we have $2x^2 = 24^2$.$2x^2 = 576$.$x^2 = 288$.The area of a right-angled triangle is given by $\frac{1}{2} 	imes 	ext{base} 	imes 	ext{height}$.Here, base $= x$ and height $= x$, so Area $= \frac{1}{2} 	imes x 	imes x = \frac{1}{2}x^2$.Substituting the value of $x^2$, we get Area $= \frac{1}{2} 	imes 288 = 144$.

In an isosceles right-angled triangle, the length of the hypotenuse is $24$. Find the area of the triangle.

Similar Questions

In $\Delta ABC$,$\overline{AB} \cong \overline{AC}$ and $\overline{AD}$ is a median. If $AD = 12$ and $BC = 18$,then the area of $\Delta ABC$ is.............

In $\Delta ABC$,the bisector of $\angle A$ intersects $\overline{BC}$ at $D$. If $AB = 12$,$AC = 8$ and $BD = 9$,find $DC$.

In $\Delta ABC$,$AB = AC$ and $m \angle A = 90^\circ$. If $BC = \sqrt{2} a$,then the area of $\Delta ABC$ is $\ldots \ldots \ldots \ldots$ $(a \in R^+)$.

In $\Delta ABC$,$m \angle B = 90^{\circ}$ and $\overline{BM}$ is an altitude to the hypotenuse $\overline{AC}$. If $AM = 4$ and $CM = 6$,then $BM = \dots$

In rhombus $ABCD$,$AC = 15$ and $BD = 36$. Find the perimeter of rhombus $ABCD$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module