Question

the base of a right angle triangle is 44m, sum of other two sides is 88m find the area of the triangle.

The answer is 726 M^2​

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Area\:of\:triangle=726\:m^{2}}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies Base \: of \: triangle = 44 \: m \\ \\ \tt: \implies Sum \: of \: other \: two \: side = 88 \: m \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies Area \: of \: triangle = ?$

• According to given question :

$\circ \: \text{Let \: perpendicular \: length \: be \: x} \\ \\ \tt \circ \: Hypotenuse =88 - x \\ \\ \tt \circ \: Base = 44 \: m \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies {h}^{2} = {p}^{2} + {b}^{2} \\ \\ \tt: \implies ({88 - x})^{2} = {x}^{2} + {44}^{2} \\ \\ \tt: \implies 7744 + {x}^{2} - 176x = {x}^{2} + 1936 \\ \\ \tt: \implies 7744 - 1936 + {x}^{2} - {x}^{2} = 176x \\ \\ \tt: \implies 176x = 5808 \\ \\ \tt: \implies x = \frac{5808}{176} \\ \\ \green{\tt: \implies x = 33 \: m} \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies Area \: of \: triangle = \frac{1}{2} \times base \times perpendicular \\ \\ \tt: \implies Area \: of \: triangle = \frac{1}{2} \times 44 \times 33 \\ \\ \tt: \implies Area \: of \: triangle = 22 \times 33 \\ \\ \green{\tt: \implies Area \: of \: triangle = 726 {m}^{2} }$

Answer 2

$\Large{\underline{\underline{\mathfrak{\bf{Question}}}}}$

The base of a right angle triangle is 44m, sum of other two sides is 88m find the area of the triangle.

The answer is 726 M²

$\Large{\underline{\underline{\mathfrak{\bf{Solution}}}}}$

$\Large{\underline{\mathfrak{\bf{Given}}}}$

• The base of a right angle triangle is 44 m
• sum of other two sides is 88 m.

$\Large{\underline{\mathfrak{\bf{Find}}}}$

• Area of right angle triangle.

$\Large{\underline{\underline{\mathfrak{\bf{Explanation}}}}}$

Let,

• perpendicular = x m

A/c to question,

( sum of other two sides is 88 m. )

➩ ( x + Hypotenuse ) = 88

➩ Hypotenuse = ( 88 -x ) m

We know,

[ Hypotenuse² = ( perpendicular² + Base²) ]

➩ (88-x)² = (x²) + ( 44²)

➩ 7744+x²-176x = x²+1936

➩ 176x = 7744 - 1936

➩ x = 5808/176 m

Now,

[ Area of triangle = 1/2 × (Base)×(perpendicular) ]

➩ Area of triangle = 1/2×(44)×(5808/176)

➩ Area of triangle = 22 × 5808/176

➩ Area of triangle = 11 × 5808 /88

➩ Area of triangle = 5808/8

➩ Area of triangle = 726 m²

Thus:-

• Area of triangle = 726 m²

That's proved