Question

The perimeter of a right angle triangle is 24 cm .If its hypotenuse is 10 cm find the area of triangle

Answer 1

hope it helps.......

Answer 2

Answer

${24cm}^{2}$

step by step deviation ,

In the questions given the perimeter of rectangle is 24cm.and hypotenuse of triangle is 10cm.

let a right angled triangle ABC . there side AB ,BC,CA.

we know that sum of all side of any object it's known as a perimeter.

now ,

AB+BC+CA = 24cm

AB + BC + 10 = 24cm

AB +BC = 24-10= 14cm

AB + BC = 14cm

we using here Pythagoras theorem,

${h}^{2} = {p}^{2} + {b}^{2}$

here , hypotenuse( AC) = 10cm

perpendicular(AB) =?

base (BC)= ?

putting in the formula

${AC}^{2} ={ AB}^{2} + {BC}^{2} \\ \\ {10}^{2} = { AB}^{2} + {BC}^{2} \\ \\ 100 = {(AB +BC )}^{2}$
here using the formula

$(a+ b)^2 = a^2 + b^2 + 2ab$

$AB^2 + BC^2+2AB.BC = 100 \\ \\ 14 + 2AB.BC = 100 \\ \\ \\ 2AB.BC = 100 - 14 \\ \\ 2AB.BC = 86 \\ \\ AB.BC = \frac{86}{2} = 48$

$Area of triangle = \frac{1}{2} \times base ×height \\ \\ \frac{1}{ \cancel2} \times \cancel48 \\ \\ 24 {cm}^{2}$

Therefore the area of triangle is ${24cm}^{2}$


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