SME
Grade 10 Math · Problem type
Rectangle and its diagonals
Use this for “A rectangle is 12 by 5. How long is each diagonal?”
Diagram
A rectangle: four right angles, opposite sides equal; the diagonals are equal and cut each other in half.
This is an example. Type your own values to start a new problem.
w
2
+
h
2
=
d
2
Formulas
w
2
+
h
2
=
d
2
12
2
+
5
2
=
13
2
Assumptions
•
A rectangle is a parallelogram with four right angles.
•
Its diagonals are congruent and bisect each other.
•
Each diagonal is the hypotenuse of a right triangle with legs w and h: d² = w² + h².
•
Lengths are in any one unit.
Step-by-step
WE KNOW
w = 12, h = 5
FIND
diagonal (d)
Step 1 · Find diagonal (d)
Use w² + h² = d²
The diagonal is the hypotenuse of a right triangle.
d
=
√
w
2
+
h
2
d
=
√
12
2
+
5
2
d
=
√
144 + 25
d
=
√
169
d
=
13
Check
Put the numbers back in. Both sides should match.
12
2
+
5
2
=
13
2
✓
Topic check
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