Rectangle diagonal from area (ACT). Game on.

Rectangle diagonal from area (ACT) is a grade 8 math skill aligned to Common Core standard 8.G.B.7: apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. Below are 1 practice questions with answers and step-by-step explanations, drawn from the 3 rectangle diagonal from area (act) problems our math games drill.

CCSS 8.G.B.73 questions in the bank
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A rectangle has length 88 centimeters and area 120120 square centimeters. What is the length of a diagonal of the rectangle, in centimeters?

Area A=ℓwA = \ell w, so 120=8w120 = 8w and w=15w = 15. The diagonal is the hypotenuse of a right triangle with legs 88 and 1515: 82+152=64+225=289=17 cm.\sqrt{8^2 + 15^2} = \sqrt{64 + 225} = \sqrt{289} = 17\text{ cm}\textsf{.}

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Tests that cover rectangle diagonal from area (act):
NAEPSBACPSAT 8/9SC READYNC EOG/EOC
Reporting domains for this skill
SAT All grades: Geometry and TrigonometryACT All grades: Preparing for Higher MathSTAAR Grade 8: Geometry and MeasurementMAP Growth Math 6+: Geometryi-Ready Grade 8: GeometrySBAC Grade 8: Concepts and Procedures
More Grade 8 skills
Linear coefficient interpretations (SAT/PSAT 8/9/10)Linear Algebra Basics: SystemsLinear functions with an unknown constantPythagorean theorem in context (SAT/ACT)Two-way tablesInterpreting linear parametersModeling linear situations (ACT/SAT/PSAT 8/9/10)Pythagorean theoremAll Grade 8 practice →

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