Question

Construct an isosceles triangle whose perimeter is $12\text{cm}$ and altitude $4\text{cm}$ and the sides of the triangle are in ratio $3:4:5.$

Answer 1

Let the triangle be $ABC$ with base $BC$ and sides $AB$ and $AC$.

Data:

Perimeter of a triangle is $12\text{cm}$
Ratio is $3:4:5$
We know, Perimeter, $P$ = sum of three sides of a triangle

$P=AB+BC+AC$

Therefore, $12=3+4+5$

$AB=\frac{3}{12}\times 12=4\text{cm}$

$BC=\frac{4}{12}\times 12=3\text{cm}$

$AC=\frac{5}{12}\times 12=5\text{cm}$

(i) Draw a line segment which is sufficiently long using ruler.

(ii) Locate points $B$ and $C$ on it such that $BC=3\text{cm}.$

(iii) With $B$ as centre and radius $4\text{cm}$, draw an arc(see figure).

(iv) With $C$ as centre and radius $5\text{cm}$, draw another arc cutting the previous arc at $C$.

(v) Join $AC$ and $AB$.

Then $△ABC$ is the required triangle.