Answer:
37 cm = 14.57 in
Step-by-step explanation:
A rectangle is a 4-sided shape with 2 pairs of congruent, parallel sides (width and length).
All interior angles of a rectangle are 90°.
The diagonal of a rectangle forms 2 congruent right triangles.
- Diagonal = hypotenuse of the right triangle
- Width and length = legs of the right triangle
Given:
- Width of rectangle = 20.8 cm
- Length of rectangle = 30.6 cm
Pythagoras Theorem
[tex]a^2+b^2=c^2[/tex]
where:
- a and b are the legs of the right triangle
- c is the hypotenuse (longest side) of the right triangle
Therefore:
- a = 20.8
- b = 30.6
- c = diagonal
Substitute the given values into the formula and solve for c:
[tex]\implies 20.8^2+30.6^=c^2[/tex]
[tex]\implies c^2=1369[/tex]
[tex]\implies c=\sqrt{1369}[/tex]
[tex]\implies c=37\:\:\sf cm[/tex]
Therefore, the length of the diagonal of the rectangle is 37 cm.
Conversion
1 inch ≈ 2.54 cm
To convert the measure of the diagonal to inches, divide 37 cm by 2.54:
[tex]\implies \dfrac{37}{2.54}=14.57 \sf \:in\:\:(2 \: d.p.)[/tex]
