Question

Construct a triangle ABC having its perimeter 12 cm and base angles 50⁰ and 70⁰

Answer 1

Perimeter of ΔABC = 12 cm
AB + BC + CA = 12 cm
∠B = 50⁰ and ∠C = 70⁰.
We are required to construct ΔABC.

Steps of construction:
Step 1. Draw a ray PX and cut off a line segment PQ=12 cm from it.
Step 2. At P, construct ∠YPB = 25⁰ with the help of protractor i. e $[\frac{1}{2}\times {50}^{\circ }]$
Step 3. At Q, construct ∠ZQP = 35⁰ i. e.$[\frac{1}{2}\times {70}^{\circ }]$
Step 4. Draw perpendicular bisectors of AP intersecting PQ at B.
Step 5. Draw perpendicular bisectors of AQ intersecting PQ at C.
Step 6. Join AB and AC.
Then, ΔABC is the required triangle.