Question

construct a triangle having the perimeter of 12.5 cm and the angle in a ratio of 3 4 5

Answer 1

Answer:

Given: Perimeter = 12.5 cm

           Ratio of angles = 3 : 4 : 5

Let, the angles are of measure 3x , 4x and 5x

then, by angle sum property of triangle

$3x+4x+5x=180\\12x=180\\x=\frac{180}{12}\\x=15$

Thus, angles are 3×15 = 45 , 4×15 = 60 and 5×15 = 75

Now for construction we have perimeter of triangle and all angles.

We use perimeter of ΔXYZ and 2 angles ∠X & ∠Y (considering them as base angle)

Follow the following steps of construction:

Step 1: Draw a line segment say LM equal to perimeter XY + YZ + XZ

Step 2: Make ∠ALM = ∠X and ∠BML = ∠Y

Step 3: Bisect ∠ALM  and ∠BML. let these bisectors intersect at a point Z (in figure 1).

Step 4: Draw perpendicular bisectors PQ of ZL and RS of ZM.

Step 5: Let PQ intersect LM at X and RS intersect LM at Y. Join XZ and YZ  (in figure 2).

Answer 2

Answer:

ΔABC, perimeter = 12.5 cm and A=∠45, B=∠60, C=∠75

Step-by-step explanation:

Given: Perimeter = 12.5 cm

Ratio of angles = 3 : 4 : 5

Consider a triangle ABC whose perimeter i.e AB+BC+AC= 12.5 cm and ∠A:∠B:∠C=3:4:5

Let ∠A=3x,∠B=4x and ∠C=5x

In ΔABC , ∠A+∠B+∠C=180°

⇒3x+4x+5x=180°

12x=180°

⇒X=15°

⇒∠A=3*15=45°

⇒∠B=4*15=60°

⇒∠C=5*15=75°

Therefore in ΔABC, perimeter = 12.5 cm and ∠A=45°, ∠B=60°, ∠C=75°