Question

The height and base of a triangle are in the rato 5:6, and the area of the triangle is 60sq.m . Find the base and height ​

Answer 1

Answer:

10m and 12m

Step-by-step explanation:

let the height and base in x

= 5x:6x

Area of triangle = 1/2 × b × h

60 = 1/2 × 5x × 6x

60 = 15x^2

60/15 = x^2

4 = x^2

√4 = x

2 = x

therefore, height = 5×2

= 10 m

And, base = 6×2

= 12m

Answer 2

$\underline{\bold{Question : }}$

$\sf{The \: height \: and \: base \: of \: a \: triangle \: are \: in \: the} \\ \sf{ratio \: 5:6 \: and \: the \: area \: of \: the \: triangle \: is \: 60} \\ \sf{sq. \: metres. \: Find \: the \: base \: and \: the \: height.}$

$\underline \bold{Solution : }$

$\sf{let \: the \: ratio \: be \ \ 5x:6x.}$

$now,$

$\begin{aligned} ar.( \triangle) \qquad \qquad \ \ &= 60 \: { \sf{m}}^{2} \\ \\ \implies \frac{1}{2} \times \small{base} \times \small{height} &= 60 \: { \sf{m}}^{2} \\ \\ \implies \frac{1}{ \cancel{2}} \times 5x \times \cancel{6}x \ {}^{3} \quad &= 60 \: { \sf{m}}^{2} \\ \\ \implies x \times x \qquad \qquad \quad&= \frac{ \cancel{60} \: {}^{ \cancel{12} \: {}^{4} } }{_1 \cancel5 \times \cancel3 _1 } \: { \sf{m}}^{2} \\ \\ \implies {x}^{2} \qquad \qquad \qquad \: \: &= 4 \: { \sf{m}}^{2} \\ \\ \implies \: x \qquad \qquad\qquad \: \: \: &= 2 \: \sf{m} \end{aligned}$

$Hence,$

• $\sf{height} = 5x = 5(2m) = 10 \: metres$
• $\sf base = 6x = 6(2m) = 12 \: metres$