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
- In $\Delta PQR$, QR is extended up to S, so that RS = RP. If $\angle RPQ = 55^\circ$ and $\angle PRS = 110^\circ$, then find the measure of $\angle PQS$.
- In a triangle, if angle $A = 30^\circ$ and angle $B = 45^\circ$, then what is the angle of C?
- The total measure of angles in a triangle is:
- ABC is a triangle. BI and CI are angle bisectors of $\angle ABC$ and $\angle ACB$. $\angle BAC = 45^\circ$. Find the measure of $\angle BIC$.
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- Write a Pythagorean triplet whose smallest member is 8.
- The lengths of two sides of a triangle are 7 cm and 8 cm respectively and the measure of the angle included between these two sides is $60^\circ$. The length (in cm) of the third side of the triangle is:
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Important Questions from Triangles
In a Δ ABC, if ∠A = 120° and AB = AC, then the values of ∠B and ∠C are respectively:
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
In ∆ABC, 2∠A = 3∠B = 6∠C. What is the value of the largest angle among these three angles?
The longest side in a right-angled triangle is called :
The sum of two sides of a triangle with the third side is
