Find the measure of the sides of an equilateral (triangle)PQR if PQ = 5x - 7 and PR = 2x + 5
If the triangle is equilateral, then:
5x - 7 = 2x + 5
Solve for x.
x=4
To find the measure of the sides of an equilateral triangle PQR, we need to set the lengths of all three sides equal to each other since an equilateral triangle has three equal sides.
Given that PQ = 5x - 7 and PR = 2x + 5, we can set these two expressions equal to each other:
5x - 7 = 2x + 5
Next, we can solve this equation for x by isolating the variable:
5x - 2x = 5 + 7
3x = 12
Dividing both sides by 3, we get:
x = 4
Now that we have the value of x, we can substitute it back into the expressions for PQ and PR to find their respective measures:
PQ = 5x - 7 = 5(4) - 7 = 20 - 7 = 13
PR = 2x + 5 = 2(4) + 5 = 8 + 5 = 13
Therefore, the measure of the sides of equilateral triangle PQR is 13 units.
To find the measure of the sides of an equilateral triangle PQR, we will use the fact that all sides of an equilateral triangle are equal in length.
Given that PQ = 5x - 7 and PR = 2x + 5, we can set them equal to each other since they represent the same side of the triangle:
5x - 7 = 2x + 5
Now, let's solve this equation for x:
5x - 2x = 5 + 7
3x = 12
Divide both sides of the equation by 3:
x = 12 / 3
x = 4
Now that we know the value of x, we can substitute it back into either PQ or PR to find the lengths of the sides.
Let's substitute x = 4 into PQ:
PQ = 5x - 7
PQ = 5(4) - 7
PQ = 20 - 7
PQ = 13
Therefore, the measure of side PQ is 13 units.
Now, let's substitute x = 4 into PR:
PR = 2x + 5
PR = 2(4) + 5
PR = 8 + 5
PR = 13
Therefore, the measure of side PR is also 13 units.
Since PQ and PR are equal in length, both sides measure 13 units.
Hence, the measure of the sides of equilateral triangle PQR is 13 units.