Question

Q3. If the angles of a triangle be in the ratio
1:4 : 5, then the ratio of the greatest
side to the smallest side is
(A) 4: (V5 - 1)
(B) 5:4
(C) (15 – 1):4
(D)
1:4​

Answer 1

Given:-

Ratio of angles of a triangle is 1:4:5

To find:-

Ratio of greatest  side to the smallest side.

Solution:-

Let the angles of the triangle be x, 4x, and 5x.

Now, x + 4x + 5x = 180°                                      (∵sum of angles of a triangle)

⇒ 10x = 180°

∴ x = $\frac{180}{10}$ = 18°

Now, ∠1 = x = 18°

        ∠2 = 4x = 4 × 18 = 72°

 and,∠3 = 5x = 5 × 18 = 90°

Separating the angles,

greatest angles = 90° and, smallest angle = 18°

Ratio of greatest side to the smallest side = $\frac{90}{18} = \frac{5}{1} = 5:1$

Hence, the required ratio = 5:1

Answer 2

Answer:

Question

If the angles of a triangle be in the ratio

1:4 : 5, then the ratio of the greatest

side to the smallest side is

Given

Ratio of Angles= 1:4:5

Solution

$\bold{◩ \purple{ \mathbb{Angle \: sum \: property}}}$

→ Sum of all interior angles in a triangle is 180°.

Let us assume the angles of triangle as 1x, 4x and 5x.

➥1x+4x+5x= 180°

➥10x= 180°

➥x= 180/10

➥x= 18

Now substitute the value of x in 1x, 4x and 5x.

✏️∠ 1x= 1 ×18= 18°

✏️∠4x= 4×18= 72°

✏️∠5= 5×18= 90°

Now the Ratio of greatest side to the smallest side is

$\to\large \bold {ratio = \frac{90}{18} } \\ \\ \to\large \bold \blue{ratio = \frac{5}{1} }$

therefore the required ratio is 5:1.

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