Question

The base of right angle triangle is 4 cm more than its height the area of the triangle is 48 square centimetres then find its base and height

Answer 1

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

$\green{\tt{\therefore{Base=12\:cm}}}$

$\green{\tt{\therefore{Height=8\:cm}}}$

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

$\green{\underline \bold{Given :}} \\ \tt: \implies Base = 4 \: cm \: more \: than \: its \: Height \\ \\ \tt: \implies Area \: of \: triangle = 48 \: {cm}^{2} \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies Base = ? \\ \\ \tt: \implies Height= ?$

• According to given question :

$\tt \circ \: Let \: Height \: be \: x \\ \\ \tt \circ \: Base = x + 4 \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies Area \: of \: triangle = \frac{1}{2} \times Base \times Height \\ \\ \tt: \implies 48 = \frac{1}{2} \times x \times (x + 4) \\ \\ \tt: \implies 48 \times 2 = {x}^{2} + 4x \\ \\ \tt: \implies {x}^{2} + 4x - 96 = 0 \\ \\ \tt: \implies {x}^{2} + 12x - 8x - 96 = 0 \\ \\ \tt: \implies x(x + 12) - 8(x + 12) = 0 \\ \\ \tt: \implies (x - 8)(x + 12) = 0 \\ \\ \green{\tt: \implies x = 8} \\ \\ \bold{Note- } \: \text{side \: of \:triangle \: cannot \: be \: in \: negative} \\ \\ \green{\tt \therefore Base = x + 4 = 12 \: cm} \\ \\ \green{\tt \therefore Height = x = 8 \: cm}$

Answer 2

Given :-

• Base = Height + 4 .
• Area of ∆ = 48cm².

To Find :-

• Height & Base of ∆ ?

Formula used :-

• Area of ∆ with Base & Height = (1/2) * Base * Height .

Solution :-

Let us Assume That, Height of ∆ is x cm.

Than, Base of ∆ will be (x + 4) cm.

So,

→ Area of ∆ = (1/2) * Base * Height .

→ (1/2) * (x + 4) * x = 48

→ x² + 4x = 48 * 2

→ x² + 4x - 96 = 0

→ x² + 12x - 8x - 96 = 0

→ x( x + 12) - 8(x + 12) = 0

→ (x + 12) (x - 8) = 0

Putting Both Equal to Zero Now,

→ x + 12 = 0

→ x = (-12) [ Negative Side ≠ ]

→ x - 8 = 0

→ x = 8 .

Hence,

→ Height of ∆ = x cm = 8cm (Ans).

→ Base of ∆ = x + 4 = 8 + 4 = 12cm (Ans).