Claire is designing a banner that will hang in her classroom. the length of one diagonal of the banner is 48 inches, and the sides are 25 inches long. is the banner a square?

it is not a square because opposite angles are not congruent.
it is not a square because the angles at the vertices are not right angles.
it is a square because all the sides are congruent.
it is a square because the diagonals are perpendicular.

answer: b is the right answer. it is not a square because the angles at the vertices are not right angles.

step-by-step explanation:

if claire's banner is a square then its internal angle must be 90°.

⇒ square must divide into two right triangles with base and perpendicular is equals to the side =25 in. and hypotenuse = diagonal of square.

by pythagoras theorem of right triangles

which is not true.

⇒ it is not a right triangle .

therefore the internal angle is not 90°.

thus,it is not a square because the angles at the vertices are not right angles.

rick has $1400 and sally has $1500

step-by-step explanation:

to find amount of money rick has after 10 years :

principal = $1000 , time = 10 years , rate = 4% annually

to find amount of money sally has after 10 years :

her friend gives to pay her $50 per year, therefore money she has after 10 years = 50 × 10 = $500

also, sally gets $1000 after 10 years,

therefore, total amount of money sally has after 10 years = 500 + 1000 = $1500

so, after 10 years : rick has $1400 and sally has $1500