One diagonal of a rhombus is tree times long as the other diagonal if the area of the rhombus is 54 square millimeters what is the length of the diagonals

The length of the diagonals are 6mm and 18mm

Step-by-step explanation:

In this question, we are tasked with calculating the lengths of the diagonals of a rhombus, given the area of the rhombus and how the two diagonals differ from each other.

Mathematically, for a rhombus, we can calculate the area of the rhombus using the formula.

A = 1/2 * d1 * d2

We are also told in the question that one diagonal is there times longer than the other.

So we can say that d1 = 3d2

hence our A becomes;

A = 1/2 * 3d2 * d2

For clarity sake, let’s call d2 d only

Hence

54 = 1/2 * 3d * d

3d^2 = 108

d^2 = 108/3

d^2 = 36

d = square root of 36

d = +6 or -6

we ignore -6 as lengthy cannot be negative

hence d = d2 = 6mm

But d1 = 3d2

d1 = 3 * 6 = 18mm

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.

d

step-by-step explanation:

i used the pitagoras theoreme