Finding Equilateral Triangle Side from Area
The problem asks us to find the side length of an equilateral triangle given its area.
We are given:
- Area of the equilateral triangle = $49\sqrt{3}\text{ cm}^2$
The formula for the area of an equilateral triangle with side 's' is:
$ \text{Area} = \frac{\sqrt{3}}{4} s^2 $
Calculating the Side Length
We can set the given area equal to the formula and solve for 's'.
- Equate the given area and the formula: $ 49\sqrt{3} = \frac{\sqrt{3}}{4} s^2 $
- Cancel out $\sqrt{3}$ from both sides of the equation: $ 49 = \frac{1}{4} s^2 $
- Multiply both sides by 4 to isolate $s^2$: $ 49 \times 4 = s^2 $ $ 196 = s^2 $
- Take the square root of both sides to find the side length 's': $ s = \sqrt{196} $ $ s = 14 $
Therefore, the side of the equilateral triangle is 14 cm.
Similar Questions
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Important Questions from Triangles
Among the following options, which are NOT sides of a triangle?
In a Δ ABC, if ∠A = 120° and AB = AC, then the values of ∠B and ∠C are respectively:
In the equilateral Δ ABC, the base BC is trisected at D and E. The line through D, Parallel to AB, meets AC at F and the line through E parallel to AC meets AB at G. If EG and DF intersect at H, then what is the ratio of the sum of the area of parallelogram AGHF and the area of the Δ DHE to the area of the Δ ABC?
The product of the perimeter of a triangle, the radius of its in‐circle, and a number gives the area of the triangle. The number is
A man goes 24 m towards east and then 10 m towards north. How far is he away from his initial position?
