The area of a rectangle shape measures 4/7 square feet if the length of the shape is 2/3 feet how wide is the rectangle

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• In triangle ABC with∠C = 90°, the sides are in the ratio BC:AC:AB = 4:3:5. If the side of middle length measures 12 cm, find: 1) The perimeter of triangle ABC; 2) The area of triangle ABC; 3) The height relative to the hypotenuse. To find the height relative to the hypotenuse, we must calculate the sides of the triangle first. The sides are in the ratio of 4:3:5, and since AC (the shorter leg) is given as the middle length at 12 cm, this represents the '3' part of the ratio. Let's find the lengths of the other two sides. For BC (shortest side), we have: BC/AC = 4/3 BC = (4/3) * 12 cm = 16 cm For AB (hypotenuse), we have: AB/AC = 5/3 AB = (5/3) * 12 cm = 20 cm Now, we know all the sides of the triangle: BC (shortest side) = 16 cm AC (middle side) = 12 cm AB (hypotenuse) = 20 cm To calculate the height to the hypotenuse (let's call it "h"), we use the area formula of a right triangle in two different ways. The area A of a right triangle is given by: A = (base * height)/2 Using sides BC and AC, we can write the area as: A = (BC * AC)/2 A = (16 cm * 12 cm)/2 A = (192 cm^2)/2 A = 96 cm^2 The same area, using the hypotenuse AB and height h, would be: A = (AB * h)/2 96 cm^2 = (20 cm * h)/2 96 cm^2 = 10 cm * h h = 96 cm^2 / 10 cm h = 9.6 cm The height relative to the hypotenuse is 9.6 cm. To address parts 1 and 2 of your problem: 1) The perimeter of triangle ABC: Perimeter = BC + AC + AB Perimeter = 16 cm + 12 cm + 20 cm Perimeter = 48 cm 2) The area of triangle ABC (which we've found during the process): Area = 96 cm^2
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