The sides of a right-angled triangle forming | vedclass

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

Question

(A) Let the perpendicular sides of the right-angled triangle be $5x$ and $12x$.According to the question,the area of the triangle is given by:$\frac{1

Vedclass · Accepted Answer

$39$

Vedclass · Answer

(A) Let the perpendicular sides of the right-angled triangle be $5x$ and $12x$.According to the question,the area of the triangle is given by:$\frac{1}{2} 	imes 	ext{base} 	imes 	ext{height} = 270 \, cm^2$$\frac{1}{2} 	imes 5x 	imes 12x = 270$$30x^2 = 270$$x^2 = \frac{270}{30} = 9$$x = 3$Now,the sides are $5 	imes 3 = 15 \, cm$ and $12 	imes 3 = 36 \, cm$.The hypotenuse is given by the Pythagorean theorem:$	ext{Hypotenuse} = \sqrt{(15)^2 + (36)^2} = \sqrt{225 + 1296} = \sqrt{1521} = 39 \, cm$.Alternatively,using the ratio $5:12:13$,the hypotenuse is $13x = 13 	imes 3 = 39 \, cm$.

The sides of a right-angled triangle forming the right angle are in the ratio $5: 12$. If the area of the triangle is $270 \, cm^2$,then the length of the hypotenuse is .......... $cm$.

Similar Questions

Find the perimeter (in $cm$) of a semicircle of radius $28\, cm$.

The perimeter of a rhombus is $60 \, cm$ and one of its diagonals is $24 \, cm$. The area (in $sq. cm$) of the rhombus is

Three circles of radius $21 \, cm$ are placed in such a way that each circle touches the other two. What is the area of the portion enclosed by the three circles? (in $sq \cdot cm$)

$A$ General,while arranging his men,who were $6000$ in number,in the form of a square,found that there were $71$ men leftover. How many were arranged in each row?

$A$ hemispherical bowl of internal diameter $54 \ cm$ contains a liquid. The liquid is to be filled in cylindrical bottles of radius $3 \ cm$ and height $9 \ cm$. How many bottles are required to empty the bowl?

Vedclass Test Series

Exam Paper Generator

Online Exam Module